Transforming higher order bright and dark solitons to the first order solitons in Kerr medium: A review

Abstract

A higher order soliton is a soliton where the initial energy is higher than the fundamental one by a specific coefficient. The value of the coefficient is square of an integer number. The intensity profile of higher order soliton (spatial or temporal) is not constant but varies periodically during propagation. The period of their evolution, called soliton-period. However, when the coefficient is not the square of an integer, the complicated intensity profile by propagation occurs. In this work, it is demonstrated and discussed the reason why higher order soliton is made, and how it modifies a factor in Nonlinear Schrödinger Equation (NLS), in positive and negative third order nonlinear (Kerr) medium. In this modified NLS equation, the exact analytical fundamental soliton solution which doesn’t show the soliton-period is obtained. Followed by numerical simulation by MATLAB, with Split-Step method, and comparison between modified initial beam-width which produces fundamental soliton and nonmodified initial beam-width that gives the other order of solitons for bright and dark solitons.